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We consider the problem of approximately solving a standard bi-quadraticprogramming (StBQP), which is NP-hard. After reformulating the original problemas an equivalent copositive tensor programming, we show how to approximate theoptimal solution by approximating the cone of copositive tensors via a serialpolyhedral cones. The established quality of approximation shows that, apolynomial time approximation scheme (PTAS) for solving StBQP exists and can beextended to solving standard multi-quadratic programming. Some numericalexamples are provided to illustrate our approach.

Error analysis of approximation algorithm for standard bi-quadratic programming